Consider three cylinders intersecting with a unit cube. Their intersection within the unit cube produces a 3-sided solid with a volume of about .386.
One cylinder has center axis (0,0,1) to (0,1,1) with unit radius, the others are rotations.
What is an exact solution for the volume?
Convert the volume integral to a surface integral: $$\int_D dV = \frac 1 3 \int_{\partial D} \mathbf r \cdot d\mathbf S.$$ Parametrize one piece of the surface as $(x, y, z) = (1 + \cos t, \sin t, z)$. The $(t, z)$ domain will be $\pi/2 < t < \pi, \,f(t) < z < g(t)$, where $f$ and $g$ are found from the equations of the other two cylinders. The integrals over the other two pieces are the same due to symmetry. This gives $$V = \int_{\pi/2}^\pi \left( \sqrt {(2 - \sin t) \sin t} + \sqrt {-(2 + \cos t) \cos t} - 1 \right) (1 + \cos t) \,dt = \\ \frac {15} 2 E {\left( \frac 1 9 \right)} - 6 K {\left( \frac 1 9 \right)} -\frac {3 \pi} 4 + 1,$$ with the elliptic integrals given in the parameter notation.